The Berg Balance Scale (BBS), named after its developer Katherine Berg, is a popular clinical test of a person's static and dynamic balance abilities. It is scored on a scale of 0 to 56 ; the higher the value, the better the score. The cut-off score is 45 , which means that a score less than 45 indicates a greater risk of falling. The file BBS_Older contains data for 20 older patients at a hospital:

The researchers then collect a new set of data, this time for 20 younger patients. Their findings are stored in the file BBS_Younger:

a. Is there evidence of a difference in the variability of the BBS values between the two age groups? (Use \(\alpha=0.05\).)

b. Determine the \(p\)-value in (a) and interpret its meaning.

c. What assumption about the population distribution of each age group is necessary in (a)? Is the assumption valid for these data?

d. Based on the results of (a), is it appropriate to use the pooledvariance \(t\) test to compare the means of the two branches?

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